I think there are many ways to do the job, depending on what equipment you have. 

One way is to use ATR-FTIR spectra

Another is using Profiling Auger/XPS

Simple solid state electronic absorption spectra may be useful if you have soundly thin films 

Dip the TiO2 in NaOH.

The Dye can be washed out by NaOH.

And measured the absorption by UV-vis. Using beer's law to calculate the concentration in NaOH 

The absorption coefficient can find in literature.